Table of Contents
- Consecutive Natural Numbers and Square Numbers
- Summary
- What’s Next?
In the previous segment, we learnt about the relationship between square numbers and odd numbers. In this segment, let us learn consecutive natural numbers and square numbers.
What is the relationship between consecutive natural numbers and ssquare numbers?
The square of an odd number can be expressed as the sum of two consecutive natural numbers. This can be generalised as,
for any odd number ‘n’, ?2 = ?2−1 + ?2+1
2 2
The table below shows the squares of five odd numbers as a sum of consecutive natural numbers applying the formula.
Odd Numbe r |
?? − ? ?? + ? ?? = + ? ? |
Sum of 2 consecutive natural numbers |
3 |
32 − 1 32 + 1 8 10 32 = + = + 2 2 2 2 |
9 = 4 + 5 |
5 |
52 − 1 52 + 1 24 25 52 = + = + 2 2 2 2 |
25 = 12 + 13 |
7 |
72 − 1 72 + 1 48 50 72 = + = + 2 2 2 2 |
49 = 24 + 25 |
9 |
92 − 1 92 + 1 80 82 92 = + = + 2 2 2 2 |
81 = 40 + 41 |
11 |
112 − 1 112 + 1 120 122 112 = + = + 2 2 2 2 |
121 = 60 + 61 |
Summary